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Duck26
@Duck26
December 2021
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Разложите квадратный трёхчлен на множители:
А) х2 + 15х + 26
Б) 4y2+3y-7
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Формула разложения кв.трехчлена на множители через корни:
ax² + bx + с = a*(x - x₁)*(x - x₂)
x² + 15x + 26 =
(x + 2)(x + 13)
найдем корни по т.Виета: x₁ = -2; x₂ = -13
4y² + 3y - 7 = 4*(y + 7/4)*(y - 1) =
(4y + 7)(y - 1)
найдем корни: D=9+4*28=11²
y₁;₂ = (-3 ⁺₋ 11)/8
y₁ = -14/8 = -7/4
y₂ = 8/8 = 1
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Answers & Comments
Verified answer
Формула разложения кв.трехчлена на множители через корни:ax² + bx + с = a*(x - x₁)*(x - x₂)
x² + 15x + 26 = (x + 2)(x + 13)
найдем корни по т.Виета: x₁ = -2; x₂ = -13
4y² + 3y - 7 = 4*(y + 7/4)*(y - 1) = (4y + 7)(y - 1)
найдем корни: D=9+4*28=11²
y₁;₂ = (-3 ⁺₋ 11)/8
y₁ = -14/8 = -7/4
y₂ = 8/8 = 1